Bell-State Preparation Simulator — Building Entanglement Step by Step Interactive

Interactive laboratory for the Hadamard-then-CNOT circuit that prepares a maximally entangled Bell pair, with step-by-step state tracking and correlated-measurement demonstration.

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About the Bell-State Preparation Simulator

A Hadamard gate on one qubit followed by a CNOT gate is the standard recipe for building maximal entanglement. This simulator steps through that exact circuit, tracking the full two-qubit state at every stage, and lets you measure the finished entangled pair to see the correlation for yourself.

What the lab covers

• A three-step circuit walkthrough: initial |00>, after Hadamard on qubit A, after CNOT(A to B). • Live probability bars for all four two-qubit outcomes (|00>, |01>, |10>, |11>) at each step. • Forward, backward and reset step controls. • A measurement button that only produces correlated results once the true Bell state (step 2) is reached. • Explicit state-equation labels describing what each step's quantum state actually is.

Pre-built scenarios

• Step to stage 1 (after Hadamard only) and note qubit A is now superposed but qubit B is still definitely |0> — no entanglement yet. • Step to stage 2 (after CNOT) and see the state become (|00>+|11>)/sqrt(2), with |01> and |10> both at 0%. • Measure the pair repeatedly (using reset and re-stepping) and confirm the two qubits' results always match — both 0 or both 1, never mixed.

Why this exact circuit matters

This two-gate sequence is the standard building block for producing entanglement on real quantum hardware and appears as a subroutine inside larger algorithms, quantum error-correction codes, and quantum communication protocols. The Quantum Teleportation lab uses exactly this recipe as its starting resource — the shared Bell pair that lets Alice and Bob transmit a qubit's state using only entanglement and two classical bits.

Frequently asked questions

What is a Bell state?

A Bell state is one of four maximally entangled two-qubit states. The one built in this lab is (|00> + |11>)/sqrt(2): measuring either qubit gives a 50/50 random result, but the two qubits' results are always perfectly correlated with each other.

Why does the circuit use Hadamard before CNOT, specifically in that order?

The Hadamard gate first puts qubit A into an equal superposition of |0> and |1>. The CNOT gate then uses that superposed qubit as its control, so the resulting flip on qubit B happens in superposition too — linking the two qubits into the entangled (|00>+|11>)/sqrt(2) state rather than a simple product state.

What happens if you measure qubit A before completing the circuit?

Before the CNOT gate is applied, qubit A and qubit B are still independent (unentangled), so measuring A only affects A — B's outcome is unrelated. Correlated results only appear once the full circuit reaches the actual Bell state, which is why this lab requires reaching step 2 (after CNOT) before allowing a measurement.

Does measuring qubit A here send information to qubit B faster than light?

No. The correlation is real, but it cannot be used to send a message, because the outcome of measuring A is genuinely random — there is no way to control what value B will show. Observers only discover the correlation exists once they compare their results afterward, over an ordinary classical channel.

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